1. **State the problem:** Solve the equation $$\frac{x}{4} - \frac{x + 6}{5} = 1$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to eliminate fractions by multiplying both sides. 3. **Find the least common denominator (LCD):** The denominators are 4 and 5, so $$\text{LCD} = 20$$. 4. **Multiply both sides by 20:** $$20 \times \left( \frac{x}{4} - \frac{x + 6}{5} \right) = 20 \times 1$$ 5. **Distribute multiplication:** $$20 \times \frac{x}{4} - 20 \times \frac{x + 6}{5} = 20$$ 6. **Simplify each term:** $$\frac{20}{4} x - \frac{20}{5} (x + 6) = 20$$ 7. **Calculate the fractions:** $$5x - 4(x + 6) = 20$$ 8. **Distribute the -4:** $$5x - 4x - 24 = 20$$ 9. **Combine like terms:** $$x - 24 = 20$$ 10. **Add 24 to both sides:** $$x - 24 + 24 = 20 + 24$$ $$x = 44$$ **Final answer:** $$x = 44$$